Nuclear magnetic resonance (NMR) has many applications in chemistry and biology. Recent advances have made it possible to use NMR to image the human body. Because much of the body is water, which gives an excellent NMR signal, NMR can yield detailed images of the body and information about various disease processes.
The physical basis of NMR is that many nuclei, such as protons, have a magnetic spin. When an external field, B.sub.0, is applied to a system whose elements have a magnetic spin, the individual elements of the system process around B.sub.0 according to the Larmor frequency. The Larmor frequency, for typical values of the external field B.sub.0 and for typical nuclei being investigated, is in the radio frequency (rf) range.
Generally, in NMR the system is perturbed by an alternating signal at or near the Larmor frequency of the spins of interest, whose magnetic field (B.sub.1) is normal to B.sub.0. This signal is called by those skilled in the art a pulse. It will perturb the spins which have a Larmor frequency at or near the frequency of the signal. The stronger the B.sub.1 field, the broader range of frequencies that it will perturb. The longer the B field is on, and the stronger the B.sub.1 filed is, the more the spins will be perturbed.
NMR imaging schemes depend on applying magnetic field gradients so that different nuclei at different locations experience different magnetic fields and, therefore, have different frequencies. Accordingly, the location of the nucleus determines its frequency One then applies a pulse, which rotates, or excites, the nuclei, and therefore, the magnetic dipole moment One tries to excite only nuclei which have frequencies corresponding to the slice of tissue which it is desired to image, and to excite those nuclei to the same degree.
Thus, it is necessary to design pulses which perturb a particular range of frequencies to the same extent but that do not perturb all other frequencies. This "ideal" pulse is physically unrealizable However, it has been possible to synthesize pulses which will do this more or less perfectly. As a result, much work in the NMR imaging art has gone into synthesizing pulses which will give very "sharp" slices, for the sharper the slice, the better the resolution of the image.
The type of "excitation" of the system may differ from one application to another. Excitation may be thought of as a rotation around some axis. In some applications, one wishes to rotate some frequencies 90.degree. around an axis in the xy plane using a .pi./2 pulse, 180.degree. around an axis in the xy plane using a .pi. pulse or inversion, and rotating all the desired frequencies 180.degree. degrees around the same axis in the xy plane using a selective refocusing pulse.
The problems of frequency selective excitation, as described above, also arises in other contexts. In many chemical applications of NMR (spectroscopy), for example, it is desired to obtain information about a chemical which is present in solution. The frequency of the nuclei of the chemical is different than the frequency of the solvent. However, because there is so much more solvent than chemical, if one excites all frequencies, the signal from the chemical will be overwhelmed. Thus, it is desirable to have a scheme where one can selectively excite frequencies which are different from the solvent frequency.
There have been two general approaches to this problem. One approach uses "hard" pulse sequences. A "hard" pulse is known by those skilled in the art to mean a constant amplitude rectangular radio frequency pulse in which the strength of the applied alternating field is sufficiently large that the pulse can be assumed to affect all frequencies of interest equally. Selective excitation is thus achieved by applying several pulses in a row and varying pulse widths and inter-pulse delay times. Different frequencies precess for different amounts during the delays between the pulses and thus respond differently to the pulse sequence. Many pulse sequences using hard pulses have been devised for different applications in NMR imaging, as described by P.J. Hore in an article entitled "Solvent Suppression in Fourier Transform Nuclear Magnetic Resonance", Journal of Magnetic Resonance, Vol. 55, pp. 283-300 (1983), for example, and by Brandes in U.S. Pat. No. 4,695,798.
However, hard pulse sequences have several major limitations. First the frequency response of hard pulses have "side lobes" or harmonics around the desired frequency range. The location of the side lobes depends on the delay between pulses. Second, if the frequency range of interest is large, as it is in NMR imaging, it may be difficult to create pulses that are strong enough to be considered "hard". Thus, they have been used primarily for solvent suppression. Furthermore, the frequency response of hard pulse sequences currently in use is far from ideal.
Another general approach has been to use "soft" pulses. A "soft" pulse is known by those skilled in the art to mean a relatively long, low amplitude pulse which is sufficiently weak that different frequencies are excited by different amounts. Because different frequencies respond differently to the same pulse, selective excitation is possible using soft pulses. These pulses also can have varying phase and amplitude and are then sometimes referred to as "shaped" pulses. Thus, when soft pulses are used, the way that different frequencies are selected is fundamentally different than when hard pulse sequences are used.
All clinical NMR imaging machines that the inventors are aware of use "soft" pulses for slice selection for routine imaging, although "hard" pulses may be used in specialized applications. However, the soft pulses currently available are far from ideal The most commonly used is the "sinc" pulse, whose shape is that of the sinc function, sin(x)/x, truncated on both sides. Unfortunately, the frequency response to this pulse is far from ideal. Not only is there a slow transition from excitation to non-excitation, but there are several side lobes of excitation within the region where excitation is not desired. This leads to reduced resolution of the images obtained.
Much work has gone into devising pulses which have better frequency characteristics. One of the best of these is the hyperbolic secant pulse described by M.S. Silver et al. in an article entitled "Highly Selective .pi./2 and .pi. Pulse Generation", Journal of Magnetic Resonance. Vol. 59, pp. 347-351 (1984). Unfortunately, even the response to this pulse does not have an ideal frequency response. Furthermore, implementation of this pulse requires a spectrometer which can simultaneously modulate the amplitude and phase of the applied external field, which many spectrometers cannot do. Indeed, patents have issued on the instrumentation for the delivery of certain shaped pulses to the transmitter, such as the afore-mentioned patent to Brandes.
There have been other continuing efforts to devise improved pulses, as described by, for example, H. Yan and J. Gore in an article entitled "Improved Selective 180.degree. Radiofrequency Pulses for Magnetization Inversion and Phase Reversal", Journal of Magnetic Resonance, Vol. 71, pp. 116-131 (1987). However, the relationship between soft and hard pulse sequences has not previously been extensively investigated. To the inventors' knowledge, there has been no previous theoretical or experimental effort using a soft pulse to approximate a hard pulse sequence, or of designing hard pulse sequences in order to design soft pulses.
In addition to the use of selective .pi./2 and .pi. pulses, one may need a selective refocusing pulse, i.e., a pulse which rotates the desired spins 180.degree. about a fixed axis in the xy plane A normal inversion pulse rotates about an axis in the xy plane and may vary with frequency. Thus, one needs to have ways of analyzing the rotation operator induced by hard pulses. One technique which is known in the NMR literature is the use of spinors, as described, for example, by L.D. Landau and E.M. Lifschitz in Quantum Mechanics: NonRelativistic Theory, pp. 188-196, Pergamon Press, London, 1965, and by I.V. Aleksandrov in The Theory of Nuclear Magnetic Resonance, pp. 169p14 181, Academic Press, NY 1966. Spinors thus allow for the representation of a hard pulse sequence so as to analyze the rotation operator. However, to the inventors' knowledge, such techniques have not been used by others for analyzing the rotation operator induced by soft pulses.
There is thus a long felt need in the art for methods of creating pulse sequences which selectively excite frequencies in NMR. This need requires construction of hard pulse sequences and soft pulses for specific excitation of the frequency spectrum so as to achieve close to optimal frequency responses. This result has not heretofore been achieved in the NMR imaging art. The present invention achieves this desired result, thereby allowing NMR and other imaging systems to produce highly resolved representations of the samples under examination.